What the original poster doesn't realise
The stereo is incoded by two orthogonal directions of movement, each involving side-to-side and up and down,one 45 degrees "left" and into the plane of the record and the other 45 degrees "right" and in.
Because they're physically orthogonal, to first order there is no crosstalk between the stereo channels, yet both use the vinyl in an equivalent way so if they deteriorate, they do so together, avoiding getting fuzz in one speaker only.
So yes, you do need 3D scanning and a good decoding algorithm.
ALternatively, use an analog system. It's called a gramophone...